Les travaux de recherche présentés dans cette thèse portent sur la méthode de décomposition de l'interaction d'échange ($J$) entre les centres magnétiques d'une molécule portant des électrons célibataires par l'approche à brisure de symétrie. Le but de cette méthode est d'extraire à l'aide des calculs non-restreints les différentes contributions physiques au couplage magnétique : l'échange direct ($J_0$) entre les orbitales magnétiques, l'échange cinétique ($\Delta J_{KE}$) permettant la délocalisation des orbitales magnétiques et la polarisation des orbitales de cœur ($\Delta J_{CP}$). La première partie de ce travail est consacrée à la théorie de la méthode de décomposition dans le cas le plus simple de deux électrons dans deux centres magnétiques d'un système centro-symétrique. La physique des contributions est expliquée en lien avec la présentation des outils méthodologiques et théoriques utilisés dans cette approche. La deuxième partie de cette thèse concerne l'implémentation de cette méthode dans le logiciel Orca et son application à des systèmes non-centrosymétriques. La dernière partie de ces travaux porte sur les développements méthodologiques que j'ai pu mener au cours de ces trois années de thèse. Une nouvelle approche permettant d'extraire la contribution de polarisation en spin est présentée. De plus, une proposition de généralisation de la décomposition de l'interaction d'échange magnétique basée sur la théorie des hamiltoniens effectifs est discutée. Un effort particulier a été porté sur l'explication et la signification physique de l'approche à brisure de symétrie dans le formalisme Hartree-Fock et la théorie de la fonctionnelle de la densité / This work is focused on the decomposition of the magnetic exchange coupling ($J$) between magnetic centers in the broken-symmetry approach. The purpose of this method is to extract from unrestricted calculations the different contributions to the magnetic coupling: the direct exchange ($J_0$) between the magnetic orbitals, the kinetic exchange interaction ($\Delta J_{KE}$) allowing the delocalization of the magnetic orbitals and the core polarization ($\Delta J_{CP}$) of non-magnetic electrons. The first part of this thesis is centered on the theory of the decomposition method in the simplest case of a centro-symmetric system with two electrons in two magnetic centers. The physical meaning is explained in relation with methodological and theoretical tools used in this approach. The second part presents the implementation of the method in the Orca package and its application to non centro-symmetric systems. In particular, this application highlights the interest of a such automatic method in standard quantum package. The last part of this work is focused on the methodological developments carried out during these three years. An innovative method avoiding the spin contamination problem is presented to extract the spin polarization effects. Furthermore, a generalization of the decomposition of $J$ to more complicated systems with more than two electrons in two magnetic centers is discussed. Special attention was given to the explanation and physical meaning of broken symmetry approach in Hartree-Fock and Density Functional Theory

No description available.

Ultracold atoms have been successfully used to study numerous systems, previously unaccessible, but a precise control over the atom number of the sample still remains a challenge. This dissertation describes our progress towards achieving Fock states of atoms. The first three chapters cover the basic physics necessary to understand the techniques we use in our lab to manipulate atoms. We then summarize our experimental results from an earlier setup where we did two experiments. In the first experiment we compare the transport of cold atoms and a Bose Einstein Condensate (BEC) in a periodic potential. We find a critical potential height beyond which the condensate behavior deviates significantly from that of thermal atoms. In the second experiment we study the effect of periodic temporal kicks by a spatially periodic potential on a BEC in a quasi one dimensional trap. We observe a limit on the energy that the system can absorb from the kicks, which we conclude is due to the finite height of the trap rather than quantum effects. The majority of the dissertation discusses our experimental setup designed to produce Fock states. The setup is designed to use the method of laser culling to produce Fock states. We are able to create a BEC and transport it into a glass cell 25 cm away. We tried different innovative methods to reduce vibrations during transport before finally settling to a commercial air bearing translation stage. We create a high confinement one dimensional optical trap using the Hermite Gaussian TEM₀₁ mode of a laser beam. Such a trap gives trapping frequencies comparable to an optical lattice and allows us to create a single one dimensional trap. We creating the TEM₀₁ mode using an appropriate phase object (phase plate) in the path of a TEM₀₀ mode beam. The method for producing the phase plate was very well controlled to obtain a good quality mode. Once the atoms are loaded into this one dimensional trap we can proceed to do laser culling to observe Sub-Poissonian number statistics and eventually create Fock states of few atoms. Finally, we describe a novel method to create a real time tunable optical lattice which would provide us with the ability of spatially resolved single atom detection. The majority of the dissertation discusses our experimental setup designed to produce Fock states. The setup is designed to use the method of laser culling to produce Fock states. We are able to create a BEC and transport it into a glass cell 25 cm away. We tried different innovative methods to reduce vibrations during tr₀ansport before finally settling to a commercial air bearing translation stage. We create a high confinement one dimensional optical trap using the Hermite Gaussian TEM₀₁ mode of a laser beam. Such a trap gives trapping frequencies comparable to an optical lattice and allows us to create a single one dimensional trap. We creating the TEM₀₁ mode using an appropriate phase object (phase plate) in the path of a TEM₀₀ mode beam. The method for producing the phase plate was very well controlled to obtain a good quality mode. Once the atoms are loaded into this one dimensional trap we can proceed to do laser culling to observe Sub-Poissonian number statistics and eventually create Fock states of few atoms. Finally, we describe a novel method to create a real time tunable optical lattice which would provide us with the ability of spatially resolved single atom detection. The majority of the dissertation discusses our experimental setup designed to produce Fock states. The setup is designed to use the method of laser culling to produce Fock states. We are able to create a BEC and transport it into a glass cell 25 cm away. We tried different innovative methods to reduce vibrations during transport before finally settling to a commercial air bearing translation stage. We create a high confinement one dimensional optical trap using the Hermite Gaussian TEM₀₁ mode of a laser beam. Such a trap gives trapping frequencies comparable to an optical lattice and allows us to create a single one dimensional trap. We creating the TEM₀₁ mode using an appropriate phase object (phase plate) in the path of a TEM₀₀ mode beam. The method for producing the phase plate was very well controlled to obtain a good quality mode. Once the atoms are loaded into this one dimensional trap we can proceed to do laser culling to observe Sub-Poissonian number statistics and eventually create Fock states of few atoms. Finally, we describe a novel method to create a real time tunable optical lattice which would provide us with the ability of spatially resolved single atom detection. The majority of the dissertation discusses our experimental setup designed to produce Fock states. The setup is designed to use the method of laser culling to produce Fock states. We are able to create a BEC and transport it into a glass cell 25 cm away. We tried different innovative methods to reduce vibrations during transport before finally settling to a commercial air bearing translation stage. We create a high confinement one dimensional optical trap using the Hermite Gaussian TEM₀₁ mode of a laser beam. Such a trap gives trapping frequencies comparable to an optical lattice and allows us to create a single one dimensional trap. We creating the TEM₀₁ mode using an appropriate phase object (phase plate) in the path of a TEM₀₀ mode beam. The method for producing the phase plate was very well controlled to obtain a good quality mode. Once the atoms are loaded into this one dimensional trap we can proceed to do laser culling to observe Sub-Poissonian number statistics and eventually create Fock states of few atoms. Finally, we describe a novel method to create a real time tunable optical lattice which would provide us with the ability of spatially resolved single atom detection. / text

The potential impact of quantum computing has stimulated a worldwide effort to develop the necessary experimental and theoretical resources. In the race for the quantum computer, several candidate systems have emerged, but the ultimate system is still unclear. We study theoretically how to realize atomic Fock states both for fermionic and bosonic atoms, mainly in one-dimensional optical traps. We demonstrate a new approach of quantum computing based on ultracold fermionic atomic Fock states in optical traps. With the Pauli exclusion principle, producing fermionic atomic Fock states in optical traps is straightforward. We find that laser culling of fermionic atoms in optical traps can produce a scalable number of ultra-high fidelity qubits. We show how each qubit can be independently prepared, and how to perform the required entanglement operations and detect the qubit states with spatially resolved, single-atom detection with adiabatic trap-splitting and fluorescence imaging. On the other hand, bosonic atoms have a strong tendency to stay together. One must rely on strong repulsive interactions to produce bosonic atomic Fock states. To simulate the physical conditions of producing Fock states with ultracold bosonic atoms, we study a many-boson system with arbitrary interaction strength using the Bethe ansatz method. This approach provides a general framework, enabling the study of Fock state production over a wide range of realistic experimental parameters. / text

Le travail présenté dans ce mémoire de thèse consiste au développement d'un modèle Hartree-Fock-Bogoliubov relativiste en symétrie axiale. Pour la première fois, un modèle de type champ moyen autocohérent relativiste incorporant explicitement les contributions d'échange est à même de décrire les noyaux atomiques déformés et superfluides. Le choix d'une formulation covariante n'est en aucun cas lié au besoin d'une cinématique nucléaire relativiste mais à l'exploitation des symétries de Lorentz. En particulier, le maintien d'une distinction entre scalaire de Lorentz et composante temporelle des 4-vecteurs est source d'efficacité et de simplification en ce qui concerne la description des systèmes nucléaires. Dans ce cadre, les nucléons sont considérés comme des particules ponctuelles représentées par un spineur de Dirac. Leur interaction dans le milieu nucléaire est decrit en terme d'échange de mésons effectifs. La dynamique de ces degrés de liberté est spécifiée par une densité lagrangienne phénoménologique, caractérisée par huit paramètres libres contraints par l'ajustement sur la masse de noyaux sphériques ainsi que par la reproduction de propriétés de la matière nucléaire. Une fonctionnelle de la densité pour l'énergie s'obtient à partir de la densité lagrangienne traitée dans l'approximation Hartree-Fock-Bogoliubov. En particulier, la prise en compte explicite des termes d'échange permet l'introduction du pion, qui ne contribue que par son terme de Fock à l'échelle du champ moyen. La minimisation de la fonctionnelle de la densité pour l'énergie conduit aux équations Hartree-Fock-Bogoliubov relativistes considérées en symétrie axiale. Ces dernières sont résolues dans une base d'oscillateur harmonique déformé. Le modèle ainsi développé est utilisé pour décrire l'état fondamental des isotopes de carbone, néon et magnésium.

Cette thèse se compose de trois chapitres. Dans le chapitre I, nous définissons les foncteurs de i-restriction et i-induction sur la catégorie O des algèbres de Hecke doublement affine rationnelles cyclotomiques. En utilisant ces foncteurs, nous construisons un cristal sur l'ensemble des classes d'isomorphisme des modules simples, qui est isomorphe au cristal de l'espace de Fock. Le chapitre II est un travail en collaboration avec Michela Varagnolo et Eric Vasserot. Nous démontrons une conjecture de Kashiwara et Miemietz sur bases canoniques et règles de branchement pour les algèbres de Hecke affines de type D. Dans le chapitre III, nous démontrons une conjecture de Leclerc et Thibon sur les multiplicités graduées associées à la filtration de Jantzen de modules de Weyl sur algèbres de v-Schur.

No description available.

Theoretical study of energy levels, oscillator strengths, transition probabilities, and lifetimes of Si III lines has been reported in this thesis. These atomic parameters are required for the interpretation of emission and absorption lines of Si III and for the modeling of astrophysical plasmas including Galactic High Velocity Clouds (HVCs), the Sun, and white dwarf stars. We used Hartree-Fock (HF) and Multiconfiguration Hartree-Fock (MCHF) methods in our calculations. We have considered 58 levels of the 3s2, 3s3p, 3p2, 3s3d, 3s4s, 3s4p, 3s4d, 3s4f, 3s5s, 3s5p, 3s5d, 3s6s, and 3s5f configurations. The relativistic corrections are included in Breit-Pauli approximation by using one-body Darwin, mass correction, spin-orbit operators, and two-body spin-other-orbit and spin-spin operators. The results have been compared with previous theoretical results and available experimental data, and generally a good agreement is found.

Im Rahmen dieser Arbeit werden theoretische Modelle zur Beschreibung von Valenz- und Rumpf-angeregten elektronischen Zuständen diskutiert. Im Fall der Valenz-Anregungen wurden time-dependend Hartree-Fock (TD-HF) und timedependent Dichtefunktionaltheorie (TD-DFT)Methoden mit verschiedenen Funktionalen für ein Perylenbisimid (PBI) System validiert. Eine einfache Analyse der Charaktäre der angeregten Zustände wurde vorgeschlagen, die auf den berechneten Übergangsdipolmomenten basiert. Dieser Ansatz ist allerdings auf Zustände beschränkt, die ein signifikantes Übergangsdipolmoment aufweisen. Deshalb wurde eine allgemeinere und fundiertere Methode entwickelt, die auf einer Analyse der berechneten CISWellenfunktion basiert. Darüberhinaus wurde ein literaturbekannter Model-Hamiltonoperator Ansatz von einem lokalisierten Molekülorbitalbild (MO) abgeleitet, das aus der generelleren Analyse-Methode resultiert. Auf diesem Weg ist ein Zugang zu diabatischen angeregten Zuständen und korrespondierenden Kopplungsparametern auf der Basis von ab initio Rechnungen gegeben. Für rumpfangeregte elektronische Zustände wurden drei Methoden für C 1s-angeregte und ionisierte Zustände verschiedener kleiner Moleküle validiert. Darüberhinaus wurde die Basissatzabhängigkeit dieser Zustände untersucht. Anhand der Resultate wurde die frozen core Näherung ausgewählt um rumpfangeregte Zustände von Naphthalintetracarbonsäuredianhydrid (NTCDA) zu berechnen. Um experimentelle Ergebnisse zu erklären, wurde ein Algorithmus entwicklet, der die Exzitonenkopplungsparameter im Fall von nicht-orthogonalen MOs berechnet. / This work focuses on theoretical approaches for predicting the valence and core excited states of aggregate systems. For the valence excitations, TD-HF and TD-DFT with different functionals have been tested at the Perylene bisimide (PBI) system. A simple character analysis method based on the calculated transition dipole moments is proposed. However, this method does not work for excited states without any transition dipole moment. Thus, we proposed a more general and more valid method based on a calculated CIS type wavefunction for the character analysis. Furthermore, a model Hamiltonian method is derived from a localized picture. The energies of the diabatic states and the corresponding coupling parameters were also determined on the basis of ab initio calculations. For the core excitation, three different methods were validated for C 1s-excited and ionized states if several small molecules. Also we tested the basis sets dependence of these core excited states. Based on those results, we chose the frozen core approximation method to evaluate the core excited states of NTCDA molecules. In order to explain the findings in the experiments, we developed an algorithm to evaluate the exciton coupling parameter where non-orthogonal MOs are used.

Neste trabalho apresentamos dois conjuntos de transformações do campo médio de emparelhamento e o cálculo deste no canal n--p isovetorial. Correlações de curto alcance são descritas numa teoria de campo médio nuclear relativístico na aproximação de Dirac-Hartree-Fock-Bogoliubov (DHFB). Esta aproximação foi desenvolvida inicialmente para descrever o dito emparelhamento padrão em matéria nuclear simétrica. A generalização da aproximação DHFB inclui o emparelhamento no canal quasideuteron em matéria assimétrica. Construímos transformações do campo de emparelhamento usando como geradores destas as matrizes $gamma$ e $ au$ e suas possíveis combinações. Existem dois conjuntos distintos que transformam de forma diferente o campo de emparelhamento. Como resultado destas transformações, obteve-se que ambos os campos de emparelhamento n--n e p--p podem ser tomados como funções reais de momento $vec{k}$. Já o cálculo do emparelhamento isovetorial n--p, baseia-se na decomposição deste campo em função dos propagadores de Gorkov. Como resultado principal, obteve-se que a inclusão de um novo vínculo $mu_{1}$ ao modelo permite soluções n--n, p--p e n--p para matéria nuclear simétrica. Fora da simetria, encontramos somente soluções n--n e p--p. Porém, nenhuma solução n--p isovetorial foi encontrada.